Highest common factor question

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In summary, the conversation discusses finding the highest common factor (HCF) of two polynomials using the Euclidean algorithm. It is considered a good technique for higher degree polynomials and may be more efficient than factoring in some cases. The conversation also mentions a previous discussion on the same topic.
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Mike012
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I was reading an older book on how to find the HCF and I wanted to know if it is a good technique or just a waste of time?

Find the highest common factor of 4x^3 - 3x^2 - 24x - 9 and 8x^3 - 2x^2 - 53x - 39

Is anyone familiar with the method? Are there better methods out there?

Thank you.
 

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This looks like the Euclidean algorithm (http://en.wikipedia.org/wiki/Greatest_common_divisor_of_two_polynomials). If so, yes it's a very good way to find the highest common factor (also known as the greatest common divisor). If the polynomials are of small enough degree, you could alternatively try to factor them and then compare their factorizations. But I think the Euclidean algorithm is better for higher degree polynomials.
 
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Closed as a duplicate of the other question.
 

FAQ: Highest common factor question

What is a highest common factor (HCF)?

A highest common factor, also known as the greatest common divisor, is the largest number that can evenly divide two or more given numbers.

How do I find the HCF of two numbers?

To find the HCF of two numbers, you can use the method of prime factorization. First, find the prime factors of each number and then determine the common factors between them. The HCF will be the product of all the common factors.

Can the HCF of two numbers be bigger than the smaller number?

No, the HCF of two numbers cannot be bigger than the smaller number. The HCF must be a factor of both numbers, so it cannot be larger than either of them.

What is the difference between HCF and LCM?

HCF (highest common factor) is the largest number that can divide two or more given numbers, while LCM (lowest common multiple) is the smallest number that is divisible by all the given numbers. In other words, HCF focuses on the common factors between the numbers, while LCM focuses on the common multiples.

Why is finding the HCF important?

Finding the HCF is important in many mathematical calculations, such as simplifying fractions, finding common denominators, and solving equations. It also helps in determining the highest possible number of equal parts that a number can be divided into.

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